The point (–2, 5) is located above the point (–2, –1).
The point (1, 212) is located to the left of the point (4, 212).
The point (3, –6) is located below the point (3, –3).
The point (−212, 1) is located to the left of the point (–3, 1).
The point (312, 12) is located to the right of the point (12, 12).
The point (2, 5) is located above the point (2, –5).
Find out the comparisons of the location of each pair of points?a. (–2, 5) is above (–2, –1). The two points have the same x-coordinate, but different y-coordinates. Since the y-coordinate increases as you move up on the coordinate plane, the point (–2, 5) is located above the point (–2, –1).
b. (1, 212) is to the left of (4, 212). The two points have the same y-coordinate, but different x-coordinates. Since the x-coordinate increases as you move to the right on the coordinate plane, the point (1, 212) is located to the left of the point (4, 212).
c. (3, –6) is below (3, –3). The two points have the same x-coordinate, but different y-coordinates. Since the y-coordinate decreases as you move down on the coordinate plane, the point (3, –6) is located below the point (3, –3).
d. (−212, 1) is to the left of (–3, 1). The two points have the same y-coordinate, but different x-coordinates. Since the x-coordinate decreases as you move to the left on the coordinate plane, the point (−212, 1) is located to the left of the point (–3, 1).
e. (312, 12) is to the right of (12, 12). The two points have the same y-coordinate, but different x-coordinates. Since the x-coordinate increases as you move to the right on the coordinate plane, the point (312, 12) is located to the right of the point (12, 12).
f. (2, 5) is above (2, –5). The two points have the same x-coordinate, but different y-coordinates. Since the y-coordinate increases as you move up on the coordinate plane, the point (2, 5) is located above the point (2, –5).
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10 problemas de ecuaciones de primer grado relacionada los datos con el cambio climático
Answer: Si la emisión de gases de efecto invernadero aumenta en un 5% anual, ¿cuánto aumentará la temperatura global en 20 años?
Solución: Dado que cada
Step-by-step explanation:
Una empresa produce 400 toneladas de dióxido de carbono al año. Si cada tonelada de dióxido de carbono contribuye al calentamiento global en 0.05 grados Celsius, ¿cuál será el aumento de temperatura causado por la empresa en un año?
Solución: 400 x 0.05 = 20 grados Celsius
La temperatura media de la Tierra ha aumentado en 1 grado Celsius desde la era preindustrial.
Si el aumento de temperatura está directamente relacionado con la cantidad de dióxido de carbono en la atmósfera, ¿cuánto dióxido de carbono adicional se ha emitido desde la era preindustrial hasta ahora?
Solución: Dado que cada tonelada de dióxido de carbono contribuye a un aumento de 0.05 grados Celsius, 1 / 0.05 = 20. Por lo tanto, se han emitido 20 veces la cantidad de dióxido de carbono necesario para contribuir a un aumento de 1 grado Celsius.
Una central térmica produce 1000 megavatios de electricidad al día. Si la eficiencia de conversión de la central térmica es del 30%, ¿cuántas toneladas de dióxido de carbono se emiten al día?
Solución: La eficiencia de conversión de la central térmica es del 30%, lo que significa que se pierde el 70% de la energía.
Por lo tanto, la cantidad de energía producida por la central térmica es de 1000 x 0.3 = 300 megavatios. Si cada megavatio produce 0.5 toneladas de dióxido de carbono, entonces la central térmica emite 300 x 0.5 = 150 toneladas de dióxido de carbono al día.
Si se reduce la emisión de dióxido de carbono en un 20%, ¿en qué medida se reducirá el aumento de temperatura global?
Solución: Si se reduce la emisión de dióxido de carbono en un 20%, se reducirá el aumento de temperatura global en un 20% x 0.05 = 0.01 grados Celsius.
Si la temperatura media en una ciudad ha aumentado en 0.5 grados Celsius en los últimos 10 años, ¿cuál es la tasa de aumento de temperatura por año?
Solución: La tasa de aumento de temperatura por año es de 0.5 grados Celsius / 10 años = 0.05 grados Celsius por año.
Si la concentración de dióxido de carbono en la atmósfera es de 400 partes por millón (ppm) y se espera que aumente en un 2% anual, ¿cuál será la concentración de dióxido de carbono en 10 años?
Solución: El aumento anual de la concentración de dióxido de carbono es de 400 x 0.02 = 8 ppm. Por lo tanto, la concentración de dióxido de carbono en 10 años será de 400 + 8 x 10 = 480 ppm.
Si la emisión de gases de efecto invernadero aumenta en un 5% anual, ¿cuánto aumentará la temperatura global en 20 años?
Solución: Dado que cada
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Aadya has 143 stamps; she gives away 11 stamps and divides the remaining equally into groups.
Sumit has 220 stamps; he gives away 11 stamps and divides the remaining equally into groups.
They end up with the same number of groups.
(a) What is the number of groups?
(b)what is the No. of stamps in each of their groups
Answer:
a) The number of groups are 11.
b) For Aadya, there are 12 stamps in each group. For Sumit, there are 19 stamps per group.
Step-by-step explanation:
Aadya: 143 - 11 = 132 stamps.
Sumit: 220 - 11 = 209 stamps.
Greatest Common Factor of 132 and 209 = 11 group for both
Aadya: Let a = # of stamps in each group.; 11a = 132; a = 12 stamps per group
Sumit: Let s = # of stamps in each group.; 11s = 209; s = 19 stamps per group.
In a recent election 59% of people supported re-electing the incumbent. Suppose a poll is done of 1230 people. If we used the normal as an approximation to the binomial, what would the mean and standard deviation be? Please show formulas used in excel
The mean is 725.7 and the standard deviation is 13.55.
To find the mean and standard deviation using the normal approximation to the binomial, we will use the following formulas in Excel:
Mean = np
Standard Deviation = sqrt(np(1-p))
Where n = sample size, p = proportion of success, and sqrt = square root.
Using the information given in the question, we can plug in the values:
n = 1230
p = 0.59
Mean = np = 1230*0.59 = 725.7
Standard Deviation = sqrt(np(1-p)) = sqrt(1230*0.59*(1-0.59)) = 13.55
Therefore, the mean is 725.7 and the standard deviation is 13.55.
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Determine whether y=3x^2 - 12x + 1 has a minimum or a maximum value. Then find the value
Minimum
-11
Step-by-step explanation:Main concepts:
Concept 1: Identify the type of equation
Concept 2: Identify the concavity (opens up/down)
Concept 3: Finding a vertex of a parabola
Concept 1: Identify the type of equation
First, observe that the equation is a polynomial. This is a type of equation where there may be multiple terms containing an x, where each term with an x is raised to a whole number power, and may be multiplied by a real number. Additionally, there may be a constant term added (or subtracted).
For our equation, [tex]y=3x^2-12x+1[/tex], the first two terms contain an x, each raised to a whole number power, and are multiplied by a number. Additionally, there is a constant added to the end of the equation. Therefore, this is a polynomial.
The largest power of x in a polynomial is called the "degree" of the polynomial. Since the largest power of x is 2, this is called a second degree polynomial. Another common name for a second degree polynomial is a quadratic equation.
This quadratic equation is already in what is known as "Standard form" [tex]y=ax^2+bx+c[/tex]
Concept 2: Identify the concavity (opens up/down)
For quadratic equations, the graph of the equation will be a sort of "U" shape" called a parabola. The parabola either opens up or down depending on the "leading coefficient" in the quadratic equation.
The "leading coefficient" of any polynomial is the constant number that is multiplied to x in the term with the highest power. In this case, the leading coefficient is 3.
A parabola opens up or down in correspondence with the sign of the leading coefficient. If the leading coefficient is positive, the parabola opens upward. If the leading coefficient is negative, the parabola opens downward.
Since the leading coefficient is 3, the parabola for our example opens upward. The branches of the "U" will go upward forever, without a maximum. However, the bottom of the "U" will have a minimum value. We are assigned to find this minimum value (how low it goes).
Concept 3: Finding a vertex of a parabola
To find the vertex of a parabola, with an equation in standard form, there are a few methods, but the most straightforward is to use the vertex formula:
[tex]h=\dfrac{-b}{2a}[/tex]
Where "h" is the x-coordinate of the vertex, and "a" and "b" are the coefficients from the quadratic equation: [tex]y=ax^2+bx+c[/tex]
[tex]h=\dfrac{-(-12)}{2(3)}[/tex]
[tex]h=\dfrac{12}{6}[/tex]
[tex]h=2[/tex]
So, the parabola will have a vertex with an x-coordinate of "2", meaning that the lowest point will be at a position that is 2 units to the right of the origin... however, we still don't know how high that minimum is. Fortunately, the equation [tex]y=3x^2-12x+1[/tex] itself gives the relationship between any x-value and the y-value that is associated with it.
[tex]y=3x^2-12x+1[/tex]
[tex]y=3(2)^2-12(2)+1[/tex]
[tex]y=3*4+(-12)*2+1[/tex]
[tex]y=12+-24+1[/tex]
[tex]y=-11[/tex]
So, the vertex of the parabola is (2,-11).
The height of the vertex is -11, so the value of the minimum is -11.
Side note: "What is the value of the minimum" is a different question that "where is the minimum at". The minimum is at 2. The actual value of the minimum is -11.
1. An oil spill is spreading such that its area is given by the exponential function A(t) = 250(1. 15)', where A is
the area in square feet and t is the time that has elapsed in days.
(b) By what percent is the oil spill increasing each
t=0?
hour?
The oil spill is increasing by approximately 0.58% per hour.
An oil spill is spreading such that its area is given by the exponential function A(t) = 250(1.15)^t, where A is the area in square feet and t is the time that has elapsed in days. To find the percent increase per hour, first convert the time from days to hours by replacing t with (t/24), since there are 24 hours in a day.
A(t) = 250(1.15)^(t/24)
To determine the hourly percent increase, find the growth factor for one hour (t=1) and subtract 1 to get the percentage:
A(1) = 250(1.15)^(1/24) ≈ 250(1.0058)
The growth factor for one hour is approximately 1.0058. To find the percent increase, subtract 1 and multiply by 100:
(1.0058 - 1) × 100 ≈ 0.58%
The oil spill is increasing by approximately 0.58% per hour.
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A circle has a diameter of 4 inches. Which statement about the area and circumference of the circle is true?
O A comparison of the area and circumference of the circle is not possible because there is not enough information to
find both.
O The numerical values of the circumference and area are equal.
O The numerical value of the circumference is greater than the numerical value of the area.
The numerical value of the circumference is less than the numerical value of the area.
Answer:
The numerical values of the circumference and area are equal
Step-by-step explanation:
Circumference: 12.57
Area: 12.57
12.57=12.57
Hope this helps! :)
Please Help Quick!!!!
Pls help immediately, and explain…
I did not do it correct pls help
Answer: x=20 y=43
Step-by-step explanation:
That little symbol in <1 means that the angle is a right angle, which is = to 90° so
<1 = 90°
133-y = 90 solve for y by subtracting 133 from both sides
-y = -43 divide by -1 on both sides
y=43
Because all 3 angles make a line, which is 180, and you know <1 = 90 then <2+<3=90 as well.
<2+<3=90
22 + x + 48 =90 simplify
70 + x =90 subtract 70 from both sides
x=20
What is the surface area of the square pyramid with base edge of 10 millimeters and a face height of 18 millimeters?
180 mm2
600 mm2
460 mm2
360 mm2
The surface area of the square base pyramid is calculated to be equal to 460 square millimetres.
How to calculate for the total surface area of the square base pyramidarea of one triangle face = 1/2 × 10 mm × 18 = 90 mm² mm
area of the four triangle faces = 4 × 90 mm² = 360 mm²
area of the square base = 10 mm × 10 mm = 100 mm²
surface area of the square base pyramid = 360 mm² + 100 mm²
surface area of the square base pyramid = 460 mm²
Therefore, the surface area of the square base pyramid is calculated to be equal to 460 square millimetres.
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What’s the answer? I need help
The two types of transformations that are produced by the matrix include:
a 90° counter clockwise rotation followed by a reflection in the vertical axis.a 90° clockwise rotation followed by a a reflection in the vertical axis.How to explain the transformationWe can see that a 90° counter-clockwise rotation followed by a dilation produces a transformation that stretches and rotates the figure.
On the other hand, a 90° counter-clockwise rotation followed by a reflection in the vertical axis produces a transformation that reflects and rotates the figure.
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Find the probability that a randomly selected within the square falls in the red shaded area
Therefore, the probability that a randomly selected point within the square falls in the red-shaded area is 68%.
What is probability?Probability is a measure of the likelihood or chance of an event occurring. It is a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event. The probability of an event A is denoted as P(A). To calculate the probability of an event, we divide the number of favorable outcomes by the total number of possible outcomes.
Here,
The area of the red-shaded region is the area of the square minus the area of the white right-angled triangle. The area of the square is the length of one side squared, which is:
Area of square = 5 cm × 5 cm
= 25 cm²
The area of the right-angled triangle is one-half the base times the perpendicular height, which is:
Area of triangle = (1/2) × base × height
= (1/2) × 4 cm × 4 cm
= 8 cm²
Therefore, the area of the red-shaded region is:
Area of red-shaded region = Area of square - Area of triangle
= 25 cm² - 8 cm²
= 17 cm²
To find the probability that a randomly selected point within the square falls in the red-shaded area, we need to divide the area of the red-shaded region by the total area of the square, which is:
Probability = Area of red-shaded region / Area of square
Probability = 17 cm² / 25 cm²
= 0.68 or 68%
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Julia works at a music store. One of her jobs is to stock new CDs on the shelf. A recent order arrived with 215 classical CDs, 125 jazz CDs, and 330 soft rock CDs. How many groups will Julia use to arrange all of the CDs?
Julia will use 10 groups to arrange all of the CDs.
To determine the number of groups Julia will use to arrange all of the CDs, we need to find the greatest common divisor of the numbers 215, 125, and 330.
First, we can check if any of the numbers are divisible by 5:
215 is not divisible by 5
125 is divisible by 5 (125 ÷ 5 = 25)
330 is divisible by 5 (330 ÷ 5 = 66)
Now we divide 125 and 330 by 5:
125 ÷ 5 = 25
330 ÷ 5 = 66
Next, we check if any of the numbers are divisible by 2:
25 is not divisible by 2
66 is divisible by 2 (66 ÷ 2 = 33)
Now we divide 66 by 2:
66 ÷ 2 = 33
Therefore, the greatest common divisor of 215, 125, and 330 is 5 × 2 = 10.
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Let E be the smallest region enclosed by the cone Z = - no Ix² + y² and the sphere x2 + y2 + z2 = 32 (note, it is the same region as in Question 8). Then, using spherical coordinates we can compute the volume of E as b d t Vol(E) = = [F(0,0,6) dø do dp, a Cs where F(0,0,0) = a = b = с = d = S = t =
the volume of the smallest region E enclosed by the cone and sphere is (64/3)π(1 - no⁴/5), where no is the constant in the equation of the cone Z = - no Ix² + y².
To compute the volume of the smallest region E enclosed by the cone and sphere, we will use spherical coordinates. In spherical coordinates, a point in 3D space is represented by three values: radius (r), polar angle (θ), and azimuthal angle (φ).
First, we need to find the intersection of the cone and sphere. Substituting Z = - no Ix² + y² into the equation of the sphere, we get x² + y² + (- no Ix² + y²)² = 32. Simplifying this equation gives us x² + y² + no²x⁴ - 2no²x²y² + y⁴ = 32. We can rewrite this equation in terms of r, θ, and φ as follows:
r²sin²θ + no²r⁴cos⁴θsin²θ - 2no²r⁴cos²θsin²θ + no²r⁴cos²θsin⁴θ = 32
Simplifying this equation gives us:
r = √(32/(sin²θ + no²cos²θsin²θ))
Next, we need to find the limits of integration for r, θ, and φ. Since the region E is enclosed by the sphere x² + y² + z² = 32, we know that the maximum value of r is 4√2. The minimum value of r is zero. The limits of integration for θ are 0 to π/2, since the cone is pointing downwards in the negative z direction. The limits of integration for φ are 0 to 2π, since the region E is symmetric about the z-axis.
The volume of the region E can be computed using the following integral:
Vol(E) = ∫∫∫ r²sinθ dr dθ dφ
Integrating over the limits of integration for r, θ, and φ, we get:
Vol(E) = ∫₀^(2π) ∫₀^(π/2) ∫₀^(4√2) r²sinθ dr dθ dφ
Evaluating this integral gives us:
Vol(E) = (64/3)π(1 - no⁴/5)
Therefore, the volume of the smallest region E enclosed by the cone and sphere is (64/3)π(1 - no⁴/5), where no is the constant in the equation of the cone Z = - no Ix² + y².
Hi! To compute the volume of the region E enclosed by the cone Z = -√(x² + y²) and the sphere x² + y² + z² = 32 using spherical coordinates, we can set up the triple integral as follows:
Vol(E) = ∫∫∫ ρ² sin(φ) dρ dθ dφ
In spherical coordinates, the cone Z = -√(x² + y²) becomes φ = 3π/4, and the sphere x² + y² + z² = 32 becomes ρ = 4.
The limits of integration are:
- ρ: 0 to 4
- θ: 0 to 2π
- φ: π/2 to 3π/4
So, the triple integral can be written as:
Vol(E) = ∫(ρ=0 to 4) ∫(θ=0 to 2π) ∫(φ=π/2 to 3π/4) ρ² sin(φ) dρ dθ dφ
By calculating this triple integral, we can find the volume of the region E.
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Which number(s) below belong to the solution set of the equation? Check all
that apply.
x + 50 = 60
A. 40
B. 60
C. 30
D. 50
E. 10
Answer:
E. 10
Step-by-step explanation:
To solve the equation x + 50 = 60, we need to isolate x on one side of the equation. Subtracting 50 from both sides, we get:
x + 50 - 50 = 60 - 50
x = 10
Therefore, the solution to the equation is x = 10. Checking the answer choices, we see that E. 10 is the only number that belongs to the solution set. Therefore, the answer is:
E. 10
hellp if you can love you
Answer:
Circumference = 56.52 cmStep-by-step explanation:
It's given that, Radius of the circle is 9 cm.
We know that Circumference of the circle is calculated as 2πr
where,
π = 3.14Substituting the required values,
Circumference = 2 × 3.14 × 9
= 6.28 × 9
= 56.52 cm
Hence the required circumference of the circle is 56.52 cm
1, 3 solve find each vault of measure. assume all segments that appear to be tangent are tangent
Hi! To solve the problem and find each vault of measure, please provide more information or a diagram, as it is unclear which geometric figure you are referring to. The terms "vault," "measure," "segments," and "tangent" can be included in the answer once more context is given.
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if an i statement is true, what is the truth value of its corresponding a statement? true false logically undetermined
If an 'I' statement is true, then the truth value of its corresponding E statement is equals to the true. So, option(a) is right answer of this problem.
Truth value : The truth value of a statement is either true or false, depending on whether the logic makes sense or not. Let us assume two statements, p : Ram goes to school daily
q : Ram will get good marks
We use implication for determining value. In logic, implication is relationship between different propositions in which the second proposition is a logical consequence of the first.
If p is true and q is true, then (p implies q) is true.If p is true and q is false, then (p implies) must be false.first case : If Ram does not go to school daily then he will get good marks. That is p is false and q is true, ¬ p --> q ⇒ true ( using implication rule)
second case : If Ram does not go to school daily then he will not get good marks. That is p is false and q is false , ¬ p --> ¬ q ⇒ true ( using implication rule)
Hence, required value of statement is true.
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Can someone please help me ASAP? It’s due tomorrow. Show work
Answer:
10 outcome is the answer
Find the value of x. round to the nearest degree.
14
5
x =
degrees
anybody knows the answer to this ?
x is approximately 20.5 degrees when rounded to the nearest degree. Therefore, x ≈ 21 degrees.
General process of solving for an unknown angle.
1. Determine the type of angle: Determine whether the angle is a right angle (90 degrees), acute (less than 90 degrees), or obtuse (greater than 90 degrees).
2. Use geometric properties: If there are geometric properties or relationships given in the problem, such as angles formed by parallel lines or within a triangle, apply those properties to find the value of x.
3. Apply trigonometric functions: If the problem involves trigonometry, use sine, cosine, or tangent functions along with the given information to solve for x.
4. Apply algebraic equations: If there is an algebraic equation involving x, set up the equation and solve for x by isolating it on one side of the equation.
To find the value of x in the given triangle, we can use the inverse tangent function, which is tan^-1.
tan(x) = opposite/adjacent
tan(x) = 5/14
To isolate x, we take the inverse tangent of both sides:
x = tan^-1(5/14)
Using a calculator, we can find that x is approximately 20.5 degrees when rounded to the nearest degree. Therefore, x ≈ 21 degrees.
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The graph of F(x), shown below, resembles the graph of G(X) = x2, but it has
been changed somewhat. Which of the following could be the equation of
F(x)?
A. F(x) = 3(x-3)2 - 3
B. Fx) = 3(x + 3)2 + 3
C. FX) = -3(x - 3)2 + 3
D. F(x) = -3(x+ 3)2 + 3
Math
Based on the graph, it appears that F(x) is a downward-facing parabola that has been shifted horizontally and vertically.
The vertex of the parabola is located at the point (3,-3), so the equation must include (x - 3) and (y + 3). Additionally, since the graph is narrower than the graph of G(x) = x^2, there must be a coefficient that is greater than 1 in front of the squared term.
Looking at the answer choices, we can eliminate options B and D because they have positive coefficients in front of the squared term, which would result in an upward-facing parabola. Option C has a negative coefficient in front of the squared term, which would result in a wider parabola than the graph shown.
Therefore, the correct answer is A, F(x) = 3(x-3)^2 - 3.
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At a hot dog eating contest, Flora ate 3 hot dogs in one minute. At this rate, how many hot dogs will Flora eat in 12 minutes? Write a proportion and solve.
Answer:36
Step-by-step explanation:
3 a minute
18 in 6 minutes
36 in 12
3:1
In the derivation of the quadratic formula by completing the square, the equation mc032-1. Jpgis created by forming a perfect square trinomial. What is the result of applying the square root property of equality to this equation?.
The result of applying the square root property of equality to this equation is x = (-b ± √(b² - 4ac)) / (2a)
If we apply the square root property of equality to the equation (x + (b/2a))² = (-4ac + b²)/(4a²), we get:
x + (b/2a) = ±√[(-4ac + b²)/(4a²)]
Next, we can simplify the expression under the square root:
√[(-4ac + b²)/(4a²)] = √(-4ac + b²)/2a
Now, we can substitute this expression back into our original equation:
x + (b/2a) = ±√(-4ac + b²)/2a
Finally, we can isolate x by subtracting (b/2a) from both sides:
x = (-b ± √(b² - 4ac)) / (2a)
This is the quadratic formula, which gives us the solutions for the quadratic equation ax² + bx + c = 0. By completing the square, we have derived this formula from the original quadratic equation.
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Complete question is:
In the derivation of the quadratic formula by completing the square, the equation (x+ (b/2a))² =(-4ac+b²)/(4a²) is created by forming a perfect square trinomial What is the result of applying the square root property of equality to this equation?
Lesson 10. 3 name two streets that appear to be parallel
Answer:
Step-by-step explanation:
where are the streets
The International Links long-distance phone company charges no monthly fee but charges 18 cents per minute for long-distance calls. The World Connections long distance company charges $50 per month plus 10 cents per minute for long-distance calls. Compare the World Connections long-distance plan to that of International Links. Under what circumstances is it cheaper to use International Links?
If the number of minutes used is less than 625 per month, it is more affordable to use International Links if not, you can go for World Connections.
Let us assume that the number of minutes used = x
Cost per minute = 18 cents
Total cost for International calls = 0.18x
Basci cahrge = 50 per month
If we use x number of minutes for calls for world connections then the total cost will be:
50 + 0.10x
To find the value of x where International Links cost is less than the total cost for World Connections
0.18x < 50 + 0.10x
0.08 < 50
8x < 50
x < 625
Therefore, we can infer that if the number of minutes used is less than 625 per month, it is cheaper to use International Links.
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I-Ready
Write and Solve Inequalities - Quiz - Level F
) The number of goldfish that can live in a small tank is at most 6.
*) Let g be the number of goldfish that can live in the tank.
Which inequality represents this situation?
9 > 6
96
g> 6
9<6
The answer is not 9 > 6, as that is a comparison between two numbers, but rather g ≤ 6, as it sets a limit on the number of goldfish that can be in the tank.
The correct inequality that represents the situation is g ≤ 6. The problem states that the maximum number of goldfish that can live in a small tank is 6, meaning that the number of goldfish must be less than or equal to 6.
The symbol ≤ represents "less than or equal to", while the symbol > represents "greater than".
Therefore, the answer is not 9 > 6, as that is a comparison between two numbers, but rather g ≤ 6, as it sets a limit on the number of goldfish that can be in the tank.
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(07.11a)marcus spent 10 hours doing his homework last week. this week he spent 11 hours doing homework. he says that he spent 110% more time doing homework this week. is he correct? show your work
Marcus is incorrect. The percentage increase in the time he spent doing homework this week compared to last week is 10%.
To determine if Marcus is correct, we need to calculate the percentage increase in the time he spent doing homework this week compared to last week.
First, we calculate the difference in hours:
11 hours - 10 hours = 1 hour
Then, we calculate the percentage increase:
(1 hour / 10 hours) x 100% = 10%
Therefore, Marcus is incorrect. The percentage increase in the time he spent doing homework this week compared to last week is 10%, not 110%.
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The temperature at sunrise was T degrees. By noon the temperature had tripled. By sunset, the temperature was only half of what the
temperature was at noon.
Which expression shows the temperature at sunset in terms of T?
OA (T+3) = Ź
(T+3)
2
Ос. 37 = 5
1 / 2
3. 37 를
D
The expression that shows the temperature at sunset in terms of T is 3T/2.
Let's call the temperature at sunrise T. According to the problem statement, the temperature tripled from sunrise to noon, so the temperature at noon is 3T.
Then, from noon to sunset, the temperature halved, so the temperature at sunset is (1/2) of the temperature at noon, or (1/2)(3T), which simplifies to 3T/2. Therefore, the expression that shows the temperature at sunset in terms of T is 3T/2.
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A building supply company sells sand by the cubic foot and by the cubic yard. The price of one cubic year of sand is $33. 75. What do you think the price of one cubic foot of sand should be? Explain answer
The price of one cubic yard of sand is $33.75, then the price of one cubic foot of sand should be $1.25.
To determine the price of one cubic foot of sand, we need to convert cubic yards to cubic feet. One cubic yard is equal to 27 cubic feet (3 feet x 3 feet x 3 feet). Therefore, if the price of one cubic yard of sand is $33.75, then the price of one cubic foot of sand should be $33.75/27 = $1.25.
This makes sense because one cubic yard contains 27 cubic feet. So, if the price of one cubic yard is $33.75, then the price per cubic foot should be 1/27th of that price.
It is important to note that this assumes the price per unit of sand remains constant regardless of the quantity purchased. In reality, bulk purchases may result in a discounted price per unit. Additionally, factors such as transportation costs and demand may also affect the price of sand.
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The value V of a classic car
appreciates exponentially and is
represented by V = 32,000(1.18)t
,
where t is the number of years
since 2020.
The rate of appreciation is
The rate of appreciation of the classic car is 18% per year.
Define exponentAn exponent is a mathematical operation that indicates how many times a number or expression is multiplied by itself. It is represented by a superscript number that is written to the right and above the base number or expression. The exponent tells us how many times the base is multiplied by itself.
The value V of the classic car appreciates exponentially, and it is represented by the formula:
V = 32,000[tex]1.18^{2}[/tex]
The term [tex]1.18^{t}[/tex] represents the factor by which the value of the car increases each year. If we calculate this factor for one year (t=1), we get:
(1.18)¹= 1.18
This means that the value of the car increases by 18% in the first year. Similarly, if we calculate the factor for two years (t=2), we get:
(1.18)² = 1.39
This means that the value of the car increases by 39% in the first two years (18% in the first year and an additional 21% in the second year).
Therefore, the rate of appreciation of the classic car is 18% per year.
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Given :f(x)=∑ n=1 ∞ (x+2) Determine: the values of x for which f(x) converges . the value of (x) if x = 1/ 1/2
a. In the geometric series for f(x) to be convergent, x < - 1
b. When x = 1¹/₂, the sum to infinity of the geometric series is f(x) = -1.4
What is a geometric series?A geometric series is the sum of terms of a geometric sequence.
a. Given the series f(x) = ∑ₙ = ₁⁰⁰(x + 2)ⁿ, we want to determine the value of x for which f(x) converges.
Now, let the general term of the sequence be Uₙ = (x + 2)ⁿ, to determine the value of x for which the series is convergent, we use the D'alembert ratio test which states that for a series to be convergent, then
Uₙ₊₁/Uₙ < 1.
So, we have that Uₙ₊₁ = (x + 2)ⁿ⁺¹
So, Uₙ₊₁/Uₙ = (x + 2)ⁿ⁺¹/ (x + 2)ⁿ
= x + 2
For convergence
Uₙ₊₁/Uₙ < 1
So,
x + 2 < 1
x < 1 - 2
x < - 1
So, for f(x) to be convergent, x < - 1
b. To find the value of f(x) when x = 1¹/₂, we proceed as folows
Since f(x) = ∑ₙ = ₁⁰⁰(x + 2)ⁿ, substituting x = 1¹/₂ = 1.5 into the equation, we have
f(x) = ∑ₙ = ₁⁰⁰(1.5 + 2)ⁿ
f(x) = ∑ₙ = ₁⁰⁰(3.5)ⁿ
= 3.5 + 3.5² + 3.5³ + ...
Since this is a geometric progression with sum to infinity, we see that the first term is a = 3.5 and the common ratio is r = ar/a = 3.5²/3.5 = 3.5
Since the sum to infinity of a geometric progression is
S₀₀ = a/(1 - r)
So, substituting the values of the variables into the equation, we have that
S₀₀ = a/(1 - r)
S₀₀ = 3.5/(1 - 3.5)
S₀₀ = 3.5/-2.5
S₀₀ = -1.4
So, when x = 1¹/₂, f(x) = -1.4
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